Evaluate
\frac{81}{41}\approx 1.975609756
Factor
\frac{3 ^ {4}}{41} = 1\frac{40}{41} = 1.975609756097561
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\begin{array}{l}\phantom{41)}\phantom{1}\\41\overline{)81}\\\end{array}
Use the 1^{st} digit 8 from dividend 81
\begin{array}{l}\phantom{41)}0\phantom{2}\\41\overline{)81}\\\end{array}
Since 8 is less than 41, use the next digit 1 from dividend 81 and add 0 to the quotient
\begin{array}{l}\phantom{41)}0\phantom{3}\\41\overline{)81}\\\end{array}
Use the 2^{nd} digit 1 from dividend 81
\begin{array}{l}\phantom{41)}01\phantom{4}\\41\overline{)81}\\\phantom{41)}\underline{\phantom{}41\phantom{}}\\\phantom{41)}40\\\end{array}
Find closest multiple of 41 to 81. We see that 1 \times 41 = 41 is the nearest. Now subtract 41 from 81 to get reminder 40. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }40
Since 40 is less than 41, stop the division. The reminder is 40. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}